The cavity method for minority games between arbitrageurs on financial markets
We use the cavity method from statistical physics for analyzing the transient and stationary dynamics of a minority game that is played by agents performing market arbitrage. On the level of linear response the method allows to include the reaction of the market to individual actions of the agents as well as the reaction of the agents to individual information items of the market. This way we derive a self-consistent solution to the minority game. In particular we analyze the impact of general nonlinear price functions on the amount of arbitrage if noise from external fluctuations is present. We identify the conditions under which arbitrage gets reduced due to the presence of noise. When the cavity method is extended to time dependent response of the market price to previous actions of the agents, the individual contributions of noise can be pursued over different time scales in the transient dynamics until a stationary state is reached and when the stationary state is reached. The contributions are from external fluctuations in price and information and from noise due to the choice of strategies. The dynamics explains the time evolution of scores of the agents' strategies: it changes from initially a random walk to non-Markovian dynamics and bounded excursions on an intermediate time scale to effectively random switching in the choice between strategies on long time scales. In contrast to the Curie-Weiss level of a mean-field approach, the market response included by the cavity method captures the realistic feature that the agents can have a preference for a certain choice of strategies without getting stuck to a single choice. The breakdown of the method in the phase transition region indicates possible market mechanisms leading to critical volatility and a possible regime shift.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Minority games played by arbitrageurs on the energy market
Along with the energy transition, the energy markets change their organization toward more decentralized and self-organized structures, striving for locally optimal profits. These tendencies may endanger the physical gri…
On the Convergence of No-Regret Dynamics in Information Retrieval Games with Proportional Ranking Functions
Publishers who publish their content on the web act strategically, in a behavior that can be modeled within the online learning framework. Regret, a central concept in machine learning, serves as a canonical measure for …
Information RetrievalRetrievalHeterogenous criticality in high frequency finance: a phase transition in flash crashes
Flash crashes in financial markets have become increasingly important attracting attention from financial regulators, market makers as well as from the media and the broader audience. Systemic risk and propagation of sho…
Comparative Evaluation of Machine Learning Approaches for Minority-Class Financial Distress Prediction Under Class Imbalance Constraints
Financial distress prediction remains a significant challenge in enterprise risk analysis due to the highly imbalanced nature of real-world financial datasets, where bankrupt or distressed firms typically constitute only…
Interpretable Machine LearningEnsemble LearningThe Elasticity of Quantitative Investment
What is the demand elasticity of statistical arbitrageurs that invest according to the advice of modern cross-sectional asset pricing models? Thirteen models from the literature exhibit strikingly inelastic demand, in co…
counterfactual